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# Re: st: sampling query

 From Richard Goldstein <[email protected]> To [email protected] Subject Re: st: sampling query Date Thu, 27 Jan 2011 17:00:55 -0500

```Steve,

thank you (and, yes, I have a copy of Kish)

Rich

On 1/27/11 4:54 PM, Steven Samuels wrote:
>
> Rich,
>
> You must compute these probabilities for every member of the combined
> sample, not just those selected in 2+ cohorts. If possible, your reading
> should include Section 11.2 "Duplicate Listings; Overlapping Frames" of
> Leslie Kish, Survey Sampling, Wiley, 1965.
>
> Steve
>
>
> Rich,
>
> Look up "multiple frames". That's a more common term for samples in
> which the ultimate unit can be reached through different trajectories
> (say landline phone sample, cell phone sample, and area/personal visit
> sample). The probabilities should be combined as
>
> 1 - Prob[ in the sample ] = product over k of (1-Prob[ reach the unit
> through the k-th frame ] )
>
> which for small probabilities leads to sum of selection probabilities.
> You are totally right that the probability should go up rather than
> down.
>
> On Thu, Jan 27, 2011 at 10:37 AM, Richard Goldstein
> <[email protected]> wrote:
>> all,
>>
>> I have received a report in which the report writer was stuck with the
>> following design (already implemented before his involvement): a number
>> of "cohorts" were set up (22 of them in fact) and the definitions of
>> these cohorts were not mutually exclusive (i.e., there was some overlap
>> in membership so that a given observation could appear in more than 1
>> cohort); to calculate the probability weights, the report writer first
>> calculated the probability of inclusion for each cohort (simply as n/N
>> where n is sample size from cohort and N is population size of cohort).
>>
>> For observations in more than one cohort, who were actually selected, he
>> then multiplied the inclusion probabilities of each cohort that
>> observations was in. Since each inclusion probability is less than 1,
>> the combined inclusion probability is smaller than the individual
>> inclusion probabilities for the individual cohort. And then, of course,
>> the weights are greater for these people (since the weight is just the
>> inverse of the inclusion probability).
>>
>> However, since these observations are in more than one cohort, shouldn't
>> the combined probability be greater for them (rather than smaller)?
>>
>> How should the combined inclusion probability be calculated?
>>
>> Or am I just wrong and the writer of the report is correct?
>>
>> Any references on dealing with overlapping "cohorts" would also be
>> greatly appreciated.
>>
>> Rich
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